A new martingale technique is developed to find formulas for the first two moments and generating function of the waiting time until one observes an element of a finite collection of patterns in a finite multi-state Markov chain.

The goal of this work is to formally abstract a Markov process evolving in discrete time over a general state space as a finite-state Markov chain, with the objective of precisely approximating its state probability distribution in time, which allows for its approximate, faster computation by that of the Markov chain. The approach is based on formal abstractions and employs an arbitrary finite ...

The basic theory of hidden Markov models was developed and applied to problems in speech recognition in the late 1960s, and has since then been applied to numerous problems, e.g. biological sequence analysis. Most applications of hidden Markov models are based on efficient algorithms for computing the probability of generating a given string, or computing the most likely path generating a given...

Risk-adjusted CUSUM schemes are designed to monitor the number of adverse outcomes following a medical procedure. An approximation of the average run length (ARL), which is the usual performance measure for a risk-adjusted CUSUM, may be found using its Markov property. We compare two methods of computing transition probability matrices where the risk model classifies patient populations into di...

In previous work we developed a method to model software testing data, including both failure events and correct behavior, as a finitestate, discrete-parameter, recurrent Markov chain. We then showed how direct computation on the Markov chain could yield various reliability related test measures. Use of the Markov chain allows us to avoid common assumptions about failure rate distributions and ...

The goal of this work is to formally abstract a Markov process evolving in discrete time over a general state space as a finite-state Markov chain, with the objective of precisely approximating its state probability distribution in time, which allows for its approximate, faster computation by that of the Markov chain. The approach is based on formal abstractions and employs an arbitrary finite ...

This article formulates a new technique for behavior analysis of systems through fuzzy Kolmogorov's differential equations and Particle Swarm Optimization. For handling the uncertainty in data, differential equations have been formulated by Markov modeling of system in fuzzy environment. First solution of these derived fuzzy Kolmogorov's differential equations has been found by Runge-Kutta four...

This paper describes a style adaptation technique using hidden semi-Markov model (HSMM) based maximum likelihood linear regression (MLLR). The HSMM-based MLLR technique can estimate regression matrices for affine transform of mean vectors of output and state duration distributions which maximize likelihood of adaptation data using EM algorithm. In this study, we apply this adaptation technique ...